Question $3.$

Donald and Joe Company has enough clay to make $24$ small vases or $6$ large vases. In other words, the large vases require $4$ times the amount of clay as the small ones. He only has enough of a special glazing compound to glaze $16$ of the small vases or $8$ of the large vases. Let $x_1$ be the number of small vases and $x_2$ be the number of large vases. The profit for the smaller vases is $$3$ each, while the larger vases is $$9$ each. If the company can sell all the vases it can produce, how many of each type should it make in order to maximize the profit?

a$.$ State the objective function

b$.$ State the constraints

c$.$ Use the corner point graphical approach

d$.$ Use the isoprofit approach